Negative Energy Densities and the Limit of Classical Space-Time

TL;DR

The paper argues that despite quantum predictions of negative energy densities, the local geometry of such regions cannot be measured classically, implying a quantum nature of space-time in these regimes.

Contribution

It introduces an operational positivity principle for energy and shows classical measurement of geometry in negative energy regions is impossible.

Findings

Negative energy densities cannot be measured via test particle trajectories.

Classical local geometry in negative energy regions is unmeasurable.

Space-time in negative energy regimes likely requires a quantum description.

Abstract

Although negative energy densities are predicted by relativistic quantum field theories, I present an argument that an "operational" positivity still holds: the energy in a region, plus the energy of an isolated device which traps or measures that energy, must be positive. If we assume Einstein's field equation, this means the local geometry of a negative energy-density region cannot be measured by the trajectories of test particles. So far, all attempts to design thought-experiments to verify a classical local geometry in the negative energy-density region have failed. It seems we must impute a quantum character to such a space-time regime.